It uses the Atmel SAM3X8E ARM Cortex-M3 CPU. It is the first 32 bit CPU in an Arduino board. Its processing speed is 84mhz, in comparison the mega 2560 that has a 16mhz processing clock speed. The Due is over 5x faster. It also has the most ram and I/O pins on the market right now, which is why it is the most expensive board.

A word of caution, some sketches need to be modified to work with the Due board as the processor is different, it also runs on 3.3v not 5v (although if you supply sufficient input voltage (i.e. 12v) there is a 5v output for shields that require 5v.

I have the nano, mega, and due and the due is by far the fastest board i'v used.

No one seems to have mentioned the Teensy, its up there with the Due and the STM32 boards.

The STM32F103 boards are roughly the same speed as the Due. Well the Due has a slightly higher clock speed but in my tests, it doesn't seem to make it any faster than the 72Mhz STM32's

I think in the near we'll get the STM32F4 boards working with the IDE, which gives clock rates up to 180Mhz. But this is still a work in progress, so only the 72Mhz STM32F103 boards are currently supported